A STUDY  OF  THE  EFFECT  OF  VARIOUS 
ELECTROLYTES  ON  ELECTRICAL 
ENDOSMOSIS 


JOHN  ARTHUR  ANDERSON 


THESIS 

FOR  THE 

DEGREE  OF  BACHELOR  OF  SCIENCE 

IN 


CHEMISTRY 


COLLEGE  OF  LIBERAL  ARTS  AND  SCIENCES 


UNIVERSITY  OF  ILLINOIS 
1922 


■ 


/&2Z 
An  2.3 


UNIVERSITY  OF  ILLINOIS 


June  1,  lp^2. 


THIS  IS  TO  CERTIFY  THAT  THE  THESIS  PREPARED  UNDER  MY  SUPERVISION  BY 


JOHN  ARTHUR  ANDERS  Oil 


entITLED  A STUDY  0F  TIIE  effects  of  various 


ELECTROLYTES  ON  ELECTRICAL  END OSMOSIS  . 


IS  APPROVED  BY  ME  AS  FULFILLING  THIS  PART  OF  THE  REQUIREMENTS  FOR  THE 
DEGREE  OF  BACHELOR  OF SCIENCI3__#__ 





Instructor  in  Charge 


Approved  : _U_  _ rC _Ur_  _ rLA  ULr. — 


Gc# . 


>'*-  '-1  HEAD  OF  DEPARTMENT  OF CHEHISTEY 


■5 — V? 


Digitized  by  the  Internet  Archive 
in  2016 


https://archive.org/details/studyofeffectofvOOande 


Acknowledgment* 


The  author  of  this  thesis  wishes  here  to  express  his 
appreciation  to  Dr.  Emmett  K.  Carver  for  continued  interest 
and  direction  during  the  study  of  this  problem. 


. 

. 


Contents 


Page 

1.  Introduction 1 

2.  Adsorption 1 

3.  Adsorption  and  the  Electrical  

Migration  of  Colloids.  5 

4.  Historical  8 

5.  Experimental 

A.  Apparatus  11 

B#  Experimental  Part • 12 

C.  Conclusions  15 

6.  Bibliography 19 

DIAGRAM  OE  APPARATUS 12 

GRAPHS 

17 


18 


1. 


1.  Introduction. 

The  purpose  of  this  study  wrs  to  rresent  the  fcctors  upon 
which  electrical  endosmesis  depends , especially  adsorption, 
and  to  check  up  experimentally  the  effect  of  ions  of  differ- 
ent valence. 


2. Adsorption. 

A great  many  solids  and  liquids  exhibit  the  property  of 
drawing  in  tightly  to  their  surfaces  other  solids  and  liquids 
and  also  gases.  This  phenomena  is  known  as  adsorption.  There 
is  only  a slight  difference  between  adsorption  rnd  absorption, 
and  that  is  in  the  point  of  view  taken  by  the  user.  For  in- 
stance , porous  charcoal  will  take  up  many  times  its  own  vol- 
ume of  some  gases.  If  we  merely  think  of  the  gases  as 
being  drav/n  into  the  mass  of  the  charcoal, we  say  that  they 
are  bei  g b sorbed, bait  if  we  think  of  the  gases  as  being 
drawn  to  the  pores  of  the  charcoal, and  concentrated  at  the 
surfaces  by  some  attractive  force  which  the  charcoal  surface 
possesses, we  call  the  phenomena  adsorption,  because  the 
word  absorption  is  too  general  a term. 

Examples  of  adsorption  are  the  removal  of  gases  from  high 
vacuum  apparatus, by  charcoal, the  removal  of  colored  impur- 
ities from  syrups  by  filtration  through  bone  black, and  the 
adsorption  of  iodine  from  sea  water  by  certain  sea  weeds  to 
which  we  are  indebted  for  our  iodine  supply. 

The  last  mentioned  example  illustrates  one  of  the  pecul- 
iarities connected  with  ads orpt ion, namely : that  some  sub- 


stances  may  "be  adsorbed  in  much  greater  proportion  than  some 

others  are.  Iodine  is  present  in  sea  water  in  very  small 

amounts, and  cannot  be  detected  by  ordinary  qualitative  tests, 

but  the  sea  weed  removes  considerable  amounts  of  it  by  adsorp 

tion, while  the  plants  seem  to  have  little  power  to  take  up 

some  of  the  salts  which  are  present  in  greater  concentration. 

In  the  same  way, hardly  any  two  substances  are  adsorbed  by  a 

1 

given  adsorbent  in  equivalent  amounts.  In  short , adsorption  is 
specific  for  any  substance , and  depends  on  a number  of  factors 

Ions  may  be  adsorbed  in  the  same  manner  as  molecular 
substances.  It  is  the  adsorption  of  ions  from  an  added  salt 
which  is  used  to  cause  the  precipitation  of  the  troublesome 
colloidal  arsenious  sulfide  solution  which  often  forms  when 
arsenic  is  precipitated  with  hydrogen  sulfide  in  anal  sis. 

The  ions  of  the  electrolyte  added  are  adsorbed, and  neutral- 
ize the  charges  on  the  colloidal  particles  of  arsenious 
sulfide.  The  particles  can  then  get  together  in  masses  which 
are  large  enough  to  settle  rapidly.  The  original  charge  on 
the  particles  is  supposed  to  cone  from  adsorption  of  ions 
from  an  excess  of  hydrogen  sulfide. 

Ion  adsorption  is  also  selective, i. e. , no  two  ions  are 
necessarily  adsorbed  in  equivalent  quantities.  For  instance, 
not  all  salts  will  cause  precipitation  of  the  colloidal 
sulfide  mentioned  above , because  there  is  not  enough  ion 
adsorbed  from  them  to  neutralize  the  charge  ontthe  particles 
of  the  sol.  Some  salts  will  cause  partial  prec ip it at ion, but 


' 

, 


' 


’ 

■ 

* 


- 

, 


5* 

none  work  so  well  as  ammonium  nitrate.  The  ions  show  an 

order  of  adsorption2  which  is  almost  the  same  for  any 

t— 

adsorbent  phase0. 


Consia.ai.acle  significance  is  attached  to  this  order  of 
adsorbtion  of  ions  and  salts,  because  of  two  striking  facts. 
Fir*o,  ^Le  amount  of  adsorption  varies  directly  as  the  valence 
of  tne  icn4.  This  has  been  called  Schulze1 s rule  of  valence, 
ilieie  are  some  exceptions  to  this  rule*-  , but  it  is  a very  use- 
approximation.  Second,  the  order  of  adsorption  of  an  ion 
is  generally  the  order  in  which  the  salt  decreases  the  surface 
tension  of  the  liquid  from  which  it  is  adsorbed0.  Some  results 
ox  Eaaglund’s  for  sodium  chloride  and  potassium  chloride  indicate 
exceptions  to  this  rule  , but  perhaps  he  is  wrong,  since  Taylor8 
gi\ss  data  for  sodium  chloride  which  contradicts  E§aglund's. 


Freundlich* s theory  of  adsorption  is  based  on  this 
generality,  that  adsorption  from  solution  varies  as  the  power 
of  the  solute  to  decrease  surface  tension.  Surface  energy  always 
tends  to  decrease,  and  one  way  in  which  it  can  decrease  is  by  a 
decrease  in  the  surface  tension.  Therefore,  if  the  tension 
between  two  Phases  decreases  with  increasing  adsorption,  then 
adsorption  will  precede  until  the  tendency  of  the  surface  energy 
to  decrease  is  balanced  by  forces  which  tend  to  promote  distrib- 
ution of  the  substance  adsorbed.  These  forces  may  come  from 
several  sources.  Bancroft  says,  "An  equilibrium  will  be  reached 
when  the  change  in  surface  tension  is  balanced  by  the  difference 


4. 

of  osmotic  pressure  between  the  surface  film  and  the  mass  of 
the  solution"*'.  In  the  case  of  adsorbed  ions,  the  forces 
opposing  adsorption  might  also  include  the  repelling  force  of 
the  charges  for  each  other  as  they  are  concentrated  by  adsorpt- 
ion"1 'h  Hatschei  gives  another  possible  source  of  charges  which 
might  oiDpose  adsorption.  It  is  based  or ji.  theory  that  whenever 
two  electrical  conductors  are  brought  together,  there  is  a 
re-distribution  of  electrons  bet¥/een  the  two  substances  which 
leaves  one  charged  positively  and  the  other  negatively.  These 
two  layers  of  electricity  might  have  an  influence  in  opposing 
adsorption  on  account  of  the  tendency  of  the  electrons  in  each 
layer  to  spread  outward.  Whatever  the  sources  of  these  forces 
opposing  adsorption  may  be  does  not  affect  the  validity  of  the 
theory  that  adsorption  consists  of  the  establishment  of  such  an 
equilibrium.  The  theory  helps  one  to  form  a concrete  picture 
of  the  mechanism  of  adsorption. 

12 

lagergren  has  a different  theory  of  adsorption,  based 
on  the  formation  of  layers  in  compression.  Surface  layers  are 
thought  to  be  in  a state  of  compression.  To  this  idea  lagergren 
has  applied  the  he  Chatelier  principle,  which  states  that  an 
increase  in  pressure  displaces  any  equilibrium  in  which  the 
volume  decreases,  and  he  has  arrived  at  the  conclusion  that 
adsorption  would  be  greater,  the  greater  the  increase  in  the 
density  of  the  surface  layer  as  adsorption  goes  on.  He  also 
concludes  that  if  a substance  decreased  the  density  of  a solution 
it  would  be  negatively  adsorbed.  Sodium  chloride  proves  to  be 
an  exception,  although  various  other  salts  support  the  theory. 


5. 

3.  Adsorption  and  the  Electrical  Migration  of  Colloids, 

The  particles  in  most  colloidal  solutions  migrate  when  in 
an  electric  field.  Gold,  silver,  and  platinum  solutions  and 
suspended  particles  of  shellac,  clay,  cotton  wool,  starch, etc. 
move  to  the  anode  in  water.  Methylene  blue,  methyl  violet, 
and  many  hydroxide  sols  of  metals  move  to  the  cathode.  There- 
fore, the  particles  in  the  former  case  must  he  charged  negatively 
and  those  in  the  latter  case,  positively.  This  phenomenon  is 
known  as  cataphoresis. 

The  source  of  the  charge  which  causes  the  migration  is 
generally  considered  to  he  the  ions  in  the  dispersing  medium 
(water  in  the  above  cases).  Air  bubbles  migrate  in  distilled 
water*'",  hut  do  not  in  turpentine  which  does  not  ionize14. 

As  to  the  mechanism  by  which  the  ions  charge  the  particles, 
there  are  two  main  theories:  the  one  based  on  the  diffusion  of 
ions  and  the  other  on  adsorption.  The  former  assumes  that  some 
ions  in  the  dispersing  medium  are  able  to  diffuse  into  the 
colloidal  phase  more  readily  than  others  and  charge  the  particles. 
The  experimental  basis  for  this  theory  is  the  fact  that  hydrogen 
ions  are  known  to  be  able  to  penetrate  aluminium  hydroxide  films, 
whereas  hydroxyl  ions  are  not.  This  theory,  however,  does  not 

fit  all  cases.  Yfhen  the  disperse  phase  is  an  air-bubble,  it 
would  not  be  consistent  to  say  , in  view  of  our  ideas  of  ions, 
that  the  bubble  becomes  charged  by  diffusion  of  ions  into  the  air. 


, 


- -> 


, 


6 


The  theory  which  does  seem  to  fit  all  cases  is  the  adsorption 
theory.  According  to  this  theory,  ions  are  drawn  to  the  surface 
of  the  particles  in  order  to  decrease  the  inter-facial  tension. 
This  charges  the  particles  and  leaves  the  dispersing  medium 
oppositely  charged.  When  the  system  is  placed  in  an  electric 
field,  the  two  phases  have  to  move  in  opposite  directions. 

ITernst  has  added  to  this  simple  adsorption  theory  with  his 

theory  of  solution  pressure  of  metals.  He  believes  that  metals 

give  off  ions  which  leaves  the  metals  charged.  The  ions,  thern- 

11 

selves,  may  be  partially  readsorbed  by  the  metal. 

If  the  charged  solid  material  is  in  the  form  of  an 

immovable  diaphragm  or  capillary  tube,  the  liquid  will  be  the 

only  movable  phase  present.  This  case  is  known  as  endosmosis. 

All  the  characteristics  of  cataphoresis  apply  equally  well  to 

endosmosis.  The  flow  nearly  always  takes  place  when  ions  are 

16 

present  in  the  liquid  used.  According  to  Perrin  a number  of 
alcohols,  nitrobenzene , and  most  salt  solutions  give  a flow, 
while  non-ionizing  substances  such  as  ether,  chloroform,  benzene, 
carbon  disulphide,  petroleum,  and  oil  of  turpentine  give  no  flow. 
Quinke,  on  the  other  hand,  found  that  both  turpentine  and  carbon 
disulphide  as  well  as  acetone  do  give  a flow.  Perhaps,  this 
can  be  explained  on  the  basis  of  impurities  in  the  materials  used 
by  Quinke  since  some  of  his  results  conflict  with  Perrin’s  and 
with  Me. Taggart’s  experiments  with  air-bubbles  in  turpentine. 
Perrin,  however,  did  find  that  acetone  did  give  a flow-1  . If 
we  neglect  these  exceptions,  endosmotic  flow  can  be  credited  to 


T 


, 


V 


ion  adsorption  in  the  same  manner  as  cataphoretic  migration, 

i.e.  that  some  ions  are  adsorbed  by  the  solid,  which  becomes 

17 

charged  with  a layer  of  electricity.  The  opposite  ions  left  in 
the  liquid  form  a second  layer  farther  from  the  solid  phase  so 
that  when  the  system  is  placed  in  an  electrical  field  this  outer 
layer  of  ions  moves  and  carries  water  through  the  capillaries 
with  it. 

If  the  charges  depend  on  the  adsorption  of  ions,  any 
change  in  the  nature  of  the  ions  available  for  adsorption  should 
have  an  effect  on  the  osmotic  flow.  In  general,  the  addition  of 
ca.tions  of  higher  valence  decreases  the  flo w to  the  highest  extent 
if  movement  is  toward  the  cathode.  In  this  case,  the  anions 
seem  to  have  no  effect.  On  the  other  hand,  the  addition  of 
anions  of  higher  valence  has  the  greatest  effect  in  decreasing 
the  flow  if  movement  is  toward  the  anode.  The  effects  of  the 
addition  of  H-ions  and  QH-ions  are  exceptions  to  this  rule. 

Both  produce  effects  far  greater  than  would  be  expected  from  a 
consideration  of  their  valence.  The  experimental  part  of  this 
study  shows  some  of  these  effects. 


, 

. * 


. 


• : It 


, . ' 


* 

. 


. 


. 


8 


4.  Historical, 


he 

In  1808,  whileAwas  investigating  the  passage  of  an 
electric  current  through  a thick  suspension  of  clay.  Reuss 
noticed  that  the  level  of  the  liquid  rose  in  one  of  the  electrode 
tubes  and  fell  in  the  other,  and  that  the  liquid  in  the  latter 
became  cloudy  with  fine  particles  of  clay.  The  other  tube 
remained  clear.  This  was  the  first  recorded  experiment  on  either 
cataphoresis  or  endosmosis. 

Reuss’  work  interested  a great  many  other  physicists 

18 

who  sought  for  an  explanation  of  the  phenomenon.  Porett 
thought  it  was  something  analogous  to  osmosis,  and  gave  the 
name  "endosmosis”  to  the  passage  of  a liquid  through  a diaphrgm 
under  the  influence  of  a drop  in  potential.  At  this  time  it 
was  noticed  that  electrolytes  added  to  the  liquid  either 
increased  or  decreased  the  flow  of  liquid  during  endosmosis. 

19 

In  1852,  Wiedeman  was  able  to  state  very  clearly 
the  most  important  generalizations  regarding  endosmosis.  These 
are  as  follows: 

1.  The  amount  of  liquid  carried  through  is 
proportional  to  the  current.  It  is 
independent  of  the  size  of  the  diaphragm 
for  a given  diaphragm  material. 


■ 


. 


* 


9 


2.  The  hydrostatic  pressure  developed  is 
proportional  to  I*  (I— Current  in  Amperes) 

3.  For  a given  diaphragm  material  the  hydro- 
static pressure  developed  is  proportional 
to  the  Current  (I)  and  independent  of 
the  dimensions  of  the  diaphragm, 

20 

Several  years  later,  Quincke  formulated. laws  for  the 
converse  of  endosmosis  where  liquid  is  forced  through  a diaphragm 
and  an  E.M.F.  is  produced.  The  statements  were  the  converse 
of  those  given  for  endosmosis. 

In  order  to  explain  endosmosis,  Quinke  and  Helmholz 
developed  the  theory  of  a double  layer  of  electricity  in  the 
interface  between  the  solid  and  liquid  phases,  i.e.,  one  kind 
of  electricity  stuck  to  the  solid,  while  the  other  kind  stayed 
in  the  liquid  part  of  the  interface.  With  a such  a double  layer 
given,  it  is  easy  to  show  that  in  an  electrical  field,  the  liquid 
and  the  solid  will  tend  to  move  and  go  in  opposite  directions. 
When  the  solid  is  held  in  place  as  in  a diaphragm,  the  liquid 
alone  will  move. 

Neither  Quinke  nor  Helmholz  could  explain  why  a double 
layer  was  formed  between  liquid  and  solid,  but  Perrin  came 
forward  with  a very  plausible  explanation.  He  said  that  the 
smaller  and  more  mobile  ions  crowded  to  the  surface  and  gave 
the  interface  its  peculiar  properties.  Freundlich  and  Bancroft 
have  enlarged  this  idea  to  the  adsorption  theory. 


10 


Some  attempts  have  "been  made  lately  to  prove  that 

the  flow  of  the  liquid  in  endosmosis  is  due  to  a hydration  of  the 
21 

ions  . If  this  were  so,  it  would  sometimes  he  necessary  for 

common  ions  to  carry  as  much  as  370  molecules  of  water  in  order 

22 

to  account  for  the  flow"  . E.W. Washburn  has  shown  that  the 
hydration  of  Ha,  li,  K,  H,  and  Mg  is  less  than  three  molecules 
of  water  per  ion.  It  seems,  therefore,  that  the  flow  through 
the  diaphragm  is  caused  by  the  layer  of  moving  ions  which  pushes 
water  through  the  capillaries. 


. • ■ 

• ' ' VC-.  •; 


11 


5,  Experimental. 

jU  Apparatus. 

The  apparatus  used  in  this  study  was  similar  to  that  of 

04 

Briggs  , except  that  the  form  was  modified  in  order  to  measure 
the  pressure  of  endosmosis  instead  of  the  flow  of  liquid. 

The  tubes  from  which  the  gauge  was  made  were  of  Pyrex 
glass,  3 mm.  in  inside  diameter.  This  size  was  chosen  because 
larger  tubes  required  too  long  a time  for  filling  and  smaller 
ones  could  not  be  obtained  of  sufficient  uniformity  for  use. 

Pieces  of  platinum,  one  cm.  square,  were  used  for 
electrodes.  They  were  placed  in  small  vertical  tubes  sealed 
to  the  horizontal  part  of  the  apparatus  so  that  the  gases  formed 
at  the  electrodes  might  escape  from  the  main  body  of  the  liquid 
and  thus  be  prevented  from  dissolving  in  the  liquid  between  the 
electrodes  and  changing  the  conductivity. 

The  substance  used  for  diaphragms  was  packed  into 
sections  of  Pyrex  tubing  3 cm.  long  and  2 cm.  in  diameter,  and 
was  held  in  place  by  plugs  of  shredded,  quantitative  filter 
paper, about  2 mm.  thick.  These  sections  were  then  inserted  into 

the  apparatus  in  which  two  Gooch  discs  prevented  the  cotton 

plugs  from  washing  out.  The  convenience  with  which  diaphragms 
can  be  made  and  inserted  is  one  of  the  advantages  of  this  type 
of  apparatus. 


♦ 


I 


' 


} 

. 


■ i,*ct  fgj 


12. 


Apparatus  for  Measuring  Endosmotic  Pressures. 


1.  Gauge  tubes 

2.  Pinch  Clamp 

3.  Gooch  Pise 

4.  Rubber  Stopper 

5.  Piaphragm 

6.  Platinum  electrodes 


IS. 

The  substances  which  are  suitable  for  diaphragms  must 
be  very  insoluble.  Barium  sulphate,  for  instance,  is  soluble 
enough  to  make  it  useless.  The  most  satisfactory  substances 
for  use  are  those  which,  in  addition  to  being  very  slightly 
soluble,  are  composed  of  hard,  smooth  grains.  With  material  of 
this  nature  , diaphragms  can  be  made  which  are  uniform;  whereas, 
if  a soft,  fibrous  substance  such  as  asbestos  is  used,  the 
diaphragms  are  not  uniform,  because  the  asbestos  can  never  be 
packed  twice  in  the  same  condition. 

Substances  which  show  stenolysis,  or  the  phenomenon  of 

precipitating  a solute  in  an  electric  field  are  to  be  avoided. 

25 

Holmes  gives  a list  of  materials  which  produce  stenolysis  and 
those  which  do  not. 

B.  Experimental  Part. 

The  following  tables  give  the  endosmotic  pressures 
obtained  with  conductivity  water  and  with  solutions  of  electro- 
lytes. 

fl)  Carborundum  Diaphragm  and  CedfO^lg. 

Molal  Concentration.  Pressure  in  cm.  on 

Cathode  Chamber. 


00000 

39 

00048 

13.2 

00144 

2.7 

00288 

-3.4 

r'Tfn 


. 

* 

* 

14. 

(2) 

Carborundum  Diaphragm  and  Ba(UOg)g. 

Molal  Concentration 

Pressure  in  cm.  on 

Cathode  Chamber. 

.000 

39 

• 008 

24.2 

.020 

6.5 

.028 

2.8 

(3) 

Carborundum  Diaphragm  and  NaCtfOs). 

.000 

39 

.008 

30.5 

.016 

15.1 

.020 

13.9 

.040 

12.3 

(4) 

Asbestos  Diaphragm  and 

h2so4. 

.000 

40.3 

• 004 

11.5 

.008 

3.7 

•*0195 

2.5 

(5) 

Asbestos  and  HC1. 

.000 

40.3 

.002 

19.4 

.006 

4.7 

15 


Substance 


(6)  Asbestos  Diaphragms  with  Organic  Electrolytes 
Molal  Cone. 


Water 

Aniline 

95%  Ethyl  Alcohol 


Pressure  in  cm.  on 
Cathode  Chamber. 

40.3 

2.4 

2.5 


C.  Conclusions. 

The  curves  on  Page  17  for  Ce(N0g)s  v Ba(U0g)2  , and 
UaltfOg  show  very  clearly  the  effect  of  the  valence  of  the  valence 
of  the  cation  in  lowering  the  endosmotic  flow  to  the  cathode. 

The  cerium  ion  has  a far  greater  effect  than  either  the  barium 
or  the  sodium  causing  even  a reversal  of  the  flow  at  a concentr- 
ation of  0.002  Molal.  The  barium  and  the  sodium  would  probably 
never  reverse  this  flow.  According  to  the  theory  of  the  adsorpt 
ion  of  ions  f the  effect  may  be  ascribed  to  an  adsorption  of 
cations  by  the  diaphragm,  the  cerium  ions  suffering  the  greatest 
adsorption  because  of  their  tri-valent  condition  while,  in  like 
manner,  the  sodium  ions  are  the  least  absorbed  because  of  their 
moni-valent  character.  This  furnishes  a check  on  the  general 
valence  rule  proposed  by  Schulze. 


The  acid  curves  on  Page  18  show  that  hydrochloric  acid 

has  approximately  the  same  effect  on  endosmose  as  has  sulphuric. 
This  agrees  with  the  general  rule  that  when  endosmose  is  taking 

place  in  the  direction  of  the  cathode,  anions  added  have  little 


16 


effect,  but  cations  have  a very  noticeable  effect.  Here,  the 
effect  of  the  sulphate  ion  and  chlorine  ion  is  so  small  in 
comparison  with  the  effect  of  the  hydrogen  ion  that  the  two  acids 
appear  to  have  the  same  influence. 


, 


. 


' 


19 


6.  Bibliography. 


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Freundlich  and  Hathansohn;  Eolloid  Z.,2£,  258, 

Schulze;  Z.  Prakt.  Chem.  25,  43,(1882)  & 27,  320,(1884 

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G.  von  Georgievies;  Monatsh.,  33,  45-62. 

Patrick;  Z.  Physik.  Chem.,  86,  545-563. 

Haaglund;  Z.  Chem.  Ind.  Kolloide,  _7*  21-22. 

Taylor;  "Chemistry  of  Colloids",  p.252,  (1920) 

Bancroft;  "Applied  Colloid  Chemistry",  p.130,  (1921) 
Hatschek  and  Willows;  "Surface  Tension  and  Surface 

Energy",  pp. 59-60,  (1915) 

w w if  i»  it  n ti 

pp. 65-66. 

Taylor;  "Chemistry  of  Colloids’;  pp. 250-252,  (1920) 

Hatschek  and  Willows;  " S.  T.  and  S.  E."  pp. 73-74. 

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